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Convex edges were used by Bark River on their kitchen series. For most people, it's easier to maintain a 'v' edge on waterstones rather than mess with sandpaper and mousepads or the expense and requirements of a belt grinder.

Note that the practice of adding a microbevel is essentially approximating a convex edge.

Convex faces yes. Final bevels on very thin edges are much more practical as flat surfaces, and I think they cut better with less resistance. I tried very thin edges with convex final edges on my first few knives and it makes them a pain to maintain. On a thicker blade I say it can work, a convex on a cleaver works well, it does offer more support to the edge. But on uber thin edges I don't think the increase in support is noticeable and cutting resistance is increased as well as sharpening time.

Convex faces yes. Final bevels on very thin edges are much more practical as flat surfaces, and I think they cut better with less resistance. I tried very thin edges with convex final edges on my first few knives and it makes them a pain to maintain. On a thicker blade I say it can work, a convex on a cleaver works well, it does offer more support to the edge. But on uber thin edges I don't think the increase in support is noticeable and cutting resistance is increased as well as sharpening time.

Convex edges will happen even if we don't want them to and that's just from our natural wobble while sharpening. I say try for a flat bevel and you'll be better off than trying to convex and getting a thick edge in the process.